# Generalizations of Prime Ideals of Semirings

## Related Articles

- On Generalized (Î±, Î²)-n-Derivations in Rings. Ashraf, Mohammad; Parveen, Nazia // Southeast Asian Bulletin of Mathematics;2016, Vol. 40 Issue 6, p783
Let R be a ring with center Z(R), Î±, Î² be endomorphisms of R. In the present paper we investigate some properties of permuting generalized (Î±, Î²)-n-derivation G of a prime or semiprime ring R associated with a permuting (Î±, Î²)-n-derivation D of R. Among some other results, we...

- On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring. SOHEILNIA, FATEMEH // Kyungpook Mathematical Journal;Mar2016, Vol. 56 Issue 1, p107
Let R be a commutative semiring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) primary ideals generalizing of 2- absorbing (resp., weakly 2-absorbing) ideals of semirings. A proper ideal I of R said to be a 2-absorbing (resp., weakly...

- A Note on Band Semirings. Zhengpan Wang; Yuanlan Zhou; Yuqi Guo // Semigroup Forum;Nov/Dec2005, Vol. 71 Issue 3, p439
The additive reduct of a band semiring is a regular band.

- Generalized Derivations and Left Ideals in Prime and Semiprime Rings. Dhara, Basudeb; Pattanayak, Atanu // ISRN Algebra;2011, Special section p1
Let R be an associative ring, Î» a nonzero left ideal of R, d : R â†’ R a derivation and G : R â†’ R a generalized derivation. In this paper, we study the following situations in prime and semiprime rings: (1) G (x o y) = a(xy Â± yx); (2) G[x, y] = a(xy Â± yx); (3) d(x) o d(y) =...

- A Zariski Topology For Semimodules. Atani, Shahabaddin Ebrahimi; Atani, Reza Ebrahimi; Tekir, Ünsal // European Journal of Pure & Applied Mathematics;2011, Vol. 4 Issue 3, p251
Given a very strong multiplication semimidule M over a commutative semiring R, a Zariski topology is defined on the spectrum Speck(M) of prime k-subsemimodules of M. The properties and possible structures of this topology are studied.

- On Exact Sequence of Semimodules over Semirings. Ninu Chaudhari, Jayprakash; Ravindra Bonde, Dipak // ISRN Algebra;2013, p1
We introduce the notion of exact sequence of semimodules over semirings using maximal homomorphisms and generalize some results of module theory to semimodules over semirings. Indeed, we prove, "If 0 â†’ Lf â†’ Mg â†’ N â†’ 0 is a split exact sequence of R-semimodules and...

- Weakly Special Radical Class and Special Radical Class of Ternary Semirings. Dutta, Tapan K.; Kar Ping Shum; Mandal, Shobhan // European Journal of Pure & Applied Mathematics;2012, Vol. 5 Issue 4, p401
In this paper, we consider the weakly special radical classes and special radical classes of ternary semirings. Some of our results are similar to those in rings theory as well as in semiring theory. In particular, the upper radicals of the above two classes are determined.

- KÃ¶the's upper nil radical for modules. Groenewald, N.; Ssevviiri, D. // Acta Mathematica Hungarica;Mar2013, Vol. 138 Issue 4, p295
Let M be a left R-module. In this paper a generalization of the notion of an s-system of rings to modules is given. Let N be a submodule of M. Define $\mathcal{S}(N):=\{ {m\in M}:\, \mbox{every } s\mbox{-system containing } m \mbox{ meets}~N \}$. It is shown that $\mathcal{S}(N)$ is equal to the...

- On the Structure of Commutative Rings with p1k1...pnkn (1â©½kiâ©½7) Zero-Divisors II. Behboodi, M.; Beyranvand, R. // European Journal of Pure & Applied Mathematics;2010, Vol. 3 Issue 4, p686
In this paper, we determine the structure of nonlocal commutative rings with p6 zerodivisors and characterize the structure of nonlocal commutative rings with p7 zero-divisors. Also, the structure and classification up to isomorphism all commutative rings with p1 k1 . . . pn kn zero-divisors,...